signal op• Data kinds: signal → signal
• Call: import fullseye as fs; fs.ledger.local_std(x, window=9) (to call the implementation directly, import dsp; dsp.local_std(x, window=9); from the registry, ops1d.get("local_std"))
Rolling standard deviation with a stated error bound.
The 1-D counterpart of the image operator `local_std` (HALCON's
`deviation_image`): the variance is taken after subtracting the mean
(`E[x^2] - E[x]^2` loses its significant digits on a signal that sits far
from zero), unbiased by `n/(n-1)`, and the residual bias of the square root
removed by `c4(n), so the estimate of sigma` itself is unbiased.
*window* is the number of samples in the sliding window, **rounded up to the
next odd number** so the window can be centred (10 becomes 11). The error
bound below is computed from the window actually used, so the number quoted
stays true. The 2-D side does the same thing — `_k(a)` snaps the knob to
3/5/7/9 — and the typed bridge that exposes this op as `tb_local_std`
scales the knob continuously, so an even value arrives whenever the knob
lands between two odd ones.
**The relative standard error of each estimate is `1/sqrt(2(n-1))`** —
35 % for a 5-sample window, 11 % for 41. Quote it next to any noise figure:
a rolling sigma over 9 samples is +- 25 %, which is wider than most of the
changes people try to read off it.
Returns an array the same length as *x* (the ends are reflected).
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• gallery2d_texture_freq — py -3.11 examples/gallery2d_texture_freq.py
signal as input)create_funct_1d_array · create_funct_1d_pairs · smooth_funct_1d_gauss · smooth_funct_1d_mean · derivate_funct_1d · integrate_funct_1d · zero_crossings_funct_1d · local_min_max_funct_1d
signal)lowpass · highpass · bandpass · envelope · rms · quantize · companding_mu_law · resample
*Provenance: dsp.py — ONED operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.